Calculated decision July 23, 2010

Dean Dad took up an interesting point: college students in remedial math have difficulty because they’ve been allowed to use calculators in high school. He then wonders if taking away the calculators is necessary. Chad Orzel responds by saying that calculators are evil (paraphrasing here) because they enable students to punch numbers without using any sort of reasoning process. (He does conclude that it may be okay to get a minimal level of competence.)

In elementary school, I was told that I was bad at math. I had the dubious distinction of having excellent math reasoning skills while having average computational skills (as measured by things like the Iowa basics tests). For most of my pre-college career, I was told I was bad at math.

When I started homeschooling the older boy, I decided I was going to do things different, especially knowing that he would likely have a similar skill set to mine. (It turns out that we’re not bad at computation, just slow. Tests which are timed in this regard thus underrepresent our actual ability.)

Elementary school teachers and sometimes junior high teachers are usually scared of math. They see math as a set of facts to be memorized and don’t really understand that reasoning is more important than computation (thanks to the advent of things like calculators).

I have never determined whether this is a cause (math-phobic types tend to go into elementary ed) or effect (teachers are only taught that math is a set of facts to memorize and doesn’t involve reasoning).

My focus, in teaching my son, was that he should learn processes and reasoning. Can he go through the process? Does he understand why we use this process? Can he figure out if the answer is wrong? Can he think of other ways to do the problem?

I guess this is why when I ask my own students simple questions about math that they can’t answer, I go slightly batty. My guess is that they’ve never had a teacher work through the reasoning aspect of math, and the students are held hostage by ‘math as an exercise only accessible by geniuses’ notion for the rest of their lives.

To be perfectly honest, I don’t think the use of calculators furthers or hinders the learning of math. It’s a red herring. The real issue is the way math is taught, or a student’s natural ability to reason. I gave my son times tables to use and he learned how to count by multiples. When he took pre-algebra in sixth grade, his teacher let him use a calculator. Initially, she was resistant, but then she later told me she let him. She said he very obviously understood the process and reasoning, but he had difficulty with computation. On the other hand, given enough time, he can do the calculations…just not as fast as his classmates.

The problem, from my view, is that the easiest way to teach math is to teach memorizable facts and perhaps simple processes. There is little reasoning taught when it’s most important: elementary school.

My son was doing a problem the other day comparing sizes of statues with their heights. He was supposed to calculate the volume of a statue when given the height along with the height and volume of a smaller replica. He went ahead and plugged numbers into the calculator, but then realized that the number he got was less than the volume of the replica. He stopped and said, “Oh! That can’t be right.” Knowing how to calculate the size is important, but being able to tell when the calculation is correct is just as important.

If all you do is memorize, then you never learn ways to check your answers or think about the process. However, it’s faster and easier just to give a table to kids and tell them to memorize things. By the time they get to junior high or high school, they may never have been taught reasoning and will therefore have no intuitive sense about numbers and the processes used the manipulate them.

You can give a kid a calculator or not. However, if you never teach them to check their work or give them ideas on questions they should be asking themselves, then the presence of a calculator will have little bearing on how well the students do in math in the long run.

I completely agree. When I started physics, I’d had no calc. I took a break from college, and when I went back, the first thing I did was take a bunch of calc before I started on my physics courses. It made a world of difference. 🙂

I’ve heard of a lot of famous physicists who have had similar issues. I guess it doesn’t bother me so much now, on a personal level, but I still get upset when I have to talk to teachers who really don’t know a thing about math.